3,060 research outputs found
An Analysis of Jitter and Transit Timing Variations in the HAT-P-13 System
If the two planets in the HAT-P-13 system are coplanar, the orbital states
provide a probe of the internal planetary structure. Previous analyses of
radial velocity and transit timing data of the system suggested that the
observational constraints on the orbital states were rather small. We reanalyze
the available data, treating the jitter as an unknown MCMC parameter, and find
that a wide range of jitter values are plausible, hence the system parameters
are less well constrained than previously suggested. For slightly increased
levels of jitter () the eccentricity of the inner planet
can be in the range , the period and eccentricity of the
outer planet can be days and
respectively, while the relative pericenter alignment, , of the planets
can take essentially any value . It is
therefore difficult to determine whether and have evolved to
a fixed-point state or a limit cycle, or to use to probe the
internal planetary structure. We perform various transit timing variation (TTV)
analyses, demonstrating that current constraints merely restrict
, and rule out relative planetary inclinations within of , but that future observations could
significantly tighten the restriction on both these parameters. We demonstrate
that TTV profiles can readily distinguish the theoretically favored
inclinations of i_{rel}=0^{\circ}\,&\,45^{\circ}, provided that sufficiently
precise and frequent transit timing observations of HAT-P-13b can be made close
to the pericenter passage of HAT-P-13c. We note the relatively high probability
that HAT-P-13c transits and suggest observational dates and strategies.Comment: Published in Ap
Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets
Theoretical studies predict that Trojans are likely a frequent byproduct of
planet formation and evolution. We examine the sensitivity of transit timing
observations for detecting Trojan companions to transiting extrasolar planets.
We demonstrate that this method offers the potential to detect terrestrial-mass
Trojans using existing ground-based observatories. We compare the transit
timing variation (TTV) method with other techniques for detecting extrasolar
Trojans and outline the future prospects for this method.Comment: submitted to ApJL, 12 pages, 2 figure
For the love of God: An analysis of the hermeneutical principles, and practices, and their development, in Augustine's On Christian Teaching, The Spirit and the Letter, The Literal Meaning of Genesis and The Enchiridion
In the history of western thought, few people are more influential than Augustine. His thought continues to impact theology, philosophy and politics, amongst other subjects, some sixteen hundred years after his death. It has been said that all western theology is a footnote to Augustine, and this is difficult to argue with. He is a man of great intellect and influence, who spoke of Scripture as the “supreme authority” (The Literal Meaning of Genesis, 4.14.25). That is why it is of interest to study how this great thinker interpreted Scripture. Augustine was not a biblical specialist like his contemporaries, Jerome or Origen. But the theological concern in his exegesis has made him a popular resource for recent biblical theologians. When asking any question of hermeneutics, the appeal of Augustine is that he reads Scripture primarily as a theologian, raising important theological questions
The Effect of Uterine Environment on Meishan and Yorkshire Fetal Development and Placental Size and Vascularity
When Meishan (M) and Yorkshire (Y) embryos were cotransferred to Y recipients that were then allowed to farrow, it was observed that the birth weights of M and Y littermates were similar averaging 1.15 ± .06 kg. In contrast, placentae matched to M piglets were markedly smaller (.70% lighter) and more vascular (.two-fold) than Y placentae. To investigate the effect of uterine environment on conceptus development to term, M and Y embryos were cotransferred to M recipients (n=3) that were slaughtered one day before expected parturition (day 113). Fetal weight, placental weight, and placental surface area were recorded. Additionally, a section of the intact maternal placental interface was excised, fixed, embedded, sectioned, and stained to allow quantitation of the placental vascular density (PVD). As observed when M and Y fetuses were cogestated by Y recipients, littermate M and Y fetuses gestated in M uteri were similar in weight (1.04 ± .03 vs. 1.03 ± .05 kg) at term. Further, M conceptuses exhibited markedly reduced (P\u3c.03) placental weights (170 ± 19 vs. 249 ± 10 g) and surface areas (1017 ± 70 vs. 1506 ± 96 cm 2 ) compared with their Y littermates. As was the case for conceptuses gestated in Y uteri, the similarity in fetal weight between the two breeds with very different placental sizes appears to result from an increased (P\u3c.09) M PVD compared with littermate Y fetuses (2.5 ± .3 vs. 1.4 ± .4%). These data indicate that in both the M and Y uterine environment, the reduced size of the M compared with Y placenta is compensated for by an increase in PVD. Currently it is unknown whether M placentae contain a greater amount of vasculature (total volume) or a similar amount of vasculature simply squeezed into a smaller space. To investigate breed differences in total placental vasculature we have perfused placentae of M and Y conceptuses cogestated in M uteri on d 113 of gestation with vascular casting material and will compare the volumes of the corrosion casts
Correction to:A Multi-stage Representation of Cell Proliferation as a Markov Process
The original version of this article unfortunately contained a mistake. It has been corrected with this correction. Equations (9) and (10) were transcribed incorrectly. Equation (9) originally read (Formula Presented.) In fact, we should first have introduced scaled variables m j = Mj ekt/C, for j = 1, . . . , k. Equation (9) should then have read (Formula Presented.).</p
Efficient choice of coloured noises in stochastic dynamics of open quantum systems
The Stochastic Liouville-von Neumann (SLN) equation describes the dynamics of
an open quantum system reduced density matrix coupled to a non-Markovian
harmonic environment. The interaction with the environment is represented by
complex coloured noises which drive the system, and whose correlation functions
are set by the properties of the environment. We present a number of schemes
capable of generating coloured noises of this kind that are built on a noise
amplitude reduction procedure [Imai et al, Chem. Phys. 446, 134 (2015)],
including two analytically optimised schemes. In doing so, we pay close
attention to the properties of the correlation functions in Fourier space,
which we derive in full. For some schemes the method of Wiener filtering for
deconvolutions leads to the realisation that weakening causality in one of the
noise correlation functions improves numerical convergence considerably,
allowing us to introduce a well controlled method for doing so. We compare the
ability of these schemes, along with an alternative optimised scheme [Schmitz
and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)], to reduce the
growth in the mean and variance of the trace of the reduced density matrix, and
their ability to extend the region in which the dynamics is stable and well
converged for a range of temperatures. By numerically optimising an additional
noise scaling freedom, we identify the scheme which performs best for the
parameters used, improving convergence by orders of magnitude and increasing
the time accessible by simulation.Comment: 23 pages, 7 figure
An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System
We report constraints on the three-dimensional orbital architecture for all
four planets known to orbit the nearby M dwarf Gliese 876 based solely on
Doppler measurements and demanding long-term orbital stability. Our dataset
incorporates publicly available radial velocities taken with the ELODIE and
CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished
HIRES velocities. We first quantitatively assess the validity of the planets
thought to orbit GJ 876 by computing the Bayes factors for a variety of
different coplanar models using an importance sampling algorithm. We find that
a four-planet model is preferred over a three-planet model. Next, we apply a
Newtonian MCMC algorithm to perform a Bayesian analysis of the planet masses
and orbits using an n-body model in three-dimensional space. Based on the
radial velocities alone, we find that a 99% credible interval provides upper
limits on the mutual inclinations for the three resonant planets
( for the "c" and "b" pair and for
the "b" and "e" pair). Subsequent dynamical integrations of our posterior
sample find that the GJ 876 planets must be roughly coplanar
( and ), suggesting the amount of
planet-planet scattering in the system has been low. We investigate the
distribution of the respective resonant arguments of each planet pair and find
that at least one argument for each planet pair and the Laplace argument
librate. The libration amplitudes in our three-dimensional orbital model
supports the idea of the outer-three planets having undergone significant past
disk migration.Comment: 19 pages, 11 figures, 8 tables. Accepted to MNRAS. Posterior samples
available at https://github.com/benelson/GJ87
- …